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Scheduling three chains on two parallel machines

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  • Agnetis, Alessandro
  • Flamini, Marta
  • Nicosia, Gaia
  • Pacifici, Andrea

Abstract

We consider the problem of scheduling n tasks subject to chain-precedence constraints on two identical machines with the objective of minimizing the makespan. The problem is known to be strongly NP-hard. Here, we prove that it is binary NP-hard even with three chains. Furthermore, we characterize the complexity of this case by presenting a pseudopolynomial time algorithm and a fully polynomial time approximation scheme.

Suggested Citation

  • Agnetis, Alessandro & Flamini, Marta & Nicosia, Gaia & Pacifici, Andrea, 2010. "Scheduling three chains on two parallel machines," European Journal of Operational Research, Elsevier, vol. 202(3), pages 669-674, May.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:3:p:669-674
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    References listed on IDEAS

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    1. J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "Complexity of Scheduling under Precedence Constraints," Operations Research, INFORMS, vol. 26(1), pages 22-35, February.
    2. Lushchakova, Irene N., 2006. "Two machine preemptive scheduling problem with release dates, equal processing times and precedence constraints," European Journal of Operational Research, Elsevier, vol. 171(1), pages 107-122, May.
    3. Herrmann, Jeffrey & Proth, Jean-Marie & Sauer, Nathalie, 1997. "Heuristics for unrelated machine scheduling with precedence constraints," European Journal of Operational Research, Elsevier, vol. 102(3), pages 528-537, November.
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    1. Agnetis, Alessandro & Kellerer, Hans & Nicosia, Gaia & Pacifici, Andrea, 2012. "Parallel dedicated machines scheduling with chain precedence constraints," European Journal of Operational Research, Elsevier, vol. 221(2), pages 296-305.
    2. Xing Chai & Wenhua Li, 2018. "Online scheduling with chain precedence constraints of equal-length jobs on parallel machines to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 472-492, August.
    3. Gaia Nicosia & Andrea Pacifici, 2017. "Scheduling assembly tasks with caterpillar precedence constraints on dedicated machines," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1680-1691, March.

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